Finding Earth's Mass Using Gauss Law

bananasplit

Is it possible to find the mass of the earth based on the earths volume mass density, roe = A-Br=R, where A = 1.42 x 104 kg/m3, B = 1.16 x 104 kg/m3, and Earth’s radius
R = 6.370 x 106 m

I know that based on Gauss Law that (closed integral) g x da = -4Gmin, where g is the total electric field due to the inside and outside of the closed surface. I don't see how this is possible.

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clem

Your equation and the units don't make sense.

bananasplit

This was the entire question
Consider a closed surface S in a region of gravitational field g. Gauss’s law for gravitation tells us that the gravitational flux through surface S is linearly proportional to the total mass min occupying the volume contained by S. More specifically, Gauss’s law states that
(closed integral)g x da = -4Gmin :
Note that g here is the total electric field, due to mass sources both inside and outside S. The value of G, the gravitational constant, is about 6.673 x10-11 N m2/kg2.
(a) Earth’s volume mass density, at any distance r from its center, is given approximately by the function p = A-Br/R, where A = 1.42 x 104 kg/m3, B = 1.16 x 104 kg/m3, and Earth’s radius R = 6.370 x 106 m. Calculate the numerical value of Earth’s mass M. Hint: The volume of a
spherical shell, lying between radii r and r + dr, is dv = 4(pie)r2dr.

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